We report mesoscopic dc current generation in an open chaotic quantum dot with ac excitation applied to one of the shape-defining gates. For excitation frequencies large compared to the inverse dwell time of electrons in the dot (i.e., GHz), we find mesoscopic fluctuations of induced current that are fully asymmetric in the applied perpendicular magnetic field, as predicted by recent theory. Conductance, measured simultaneously, is found to be symmetric in field. In the adiabatic (i.e., MHz) regime, in contrast, the induced current is always symmetric in field, suggesting its origin is mesoscopic rectification.